ALEXANDRA, SOUTH AFRICA (USA TODAY)--Tucked behind a black steel gate and a partially collapsed cement wall with barbed wire sits Nelson Mandela's first house when he moved to Johannesburg in 1940.

A pile of garbage and a giant nylon bag full of empty bottles stand at the entrance to the courtyard with its dirt paths and crumbled patches of concrete. Most nearby houses have no electricity or indoor plumbing. People use buckets to haul water from a communal tap and use outhouses, called long drops, that they lock, so no one steals the metal toilets inside.

In some parts of this sprawling township, the conditions are not much different from what Mandela described in his autobiography about his time here: "It was no more than a shack with a dirt floor, no heat, no electricity, no running water. But it was a place of my own and I was happy to have it."

Two miles away, past the boulevard where hawkers line the sidewalk selling fruits, vegetables, hats, sunglasses, goats and cellphone minutes, lies Sandton. The well-heeled suburb is home to a swanky mall, gated apartment complexes, the South African stock exchange and an Aston Martin dealership.

It is a place to which many aspire, especially those who lived under the oppressive rule of apartheid when blacks couldn't own land or were forced out of their homes indiscriminately.

The disparity between abject poverty and great wealth that is evident in Alexandra and Sandton is representative of a growing income inequality throughout South Africa since the end of apartheid. The World Bank says the rich-poor gap in South Africa is among the world's worst.

"Sandton and Alexandra are the most extreme example of this, but we've had increasing inequality over the last 20 years," says Adam Habib, a political science professor and vice chancellor at the University of Witwatersrand in Johannesburg. "That's what's so striking."

Habib blames the inequality in part on the legacy of apartheid and says it was made worse by a conservative economic agenda in which the government privatized services and deregulated industries. He says investments in education and manufacturing are ways to reduce inequality.

"Income inequality is particularly dangerous," he says, because it can lead to violent crime and other social ills. "And that's what we are seeing in South Africa now," he says.

Alexandra, known as Alex, was a special place for Mandela, but it is one of the poorest and roughest areas of Johannesburg. Here, where most families cram into one-room shacks wide enough to fit only one small bed, where people are jobless and mill about the streets and where crime is so rampant no one goes out after dark, Nelson Mandela's promise for a better life has fallen short.

Now that he's dead, residents have little faith the government will help improve their lives.

"Those guys in the government respected him," says Mawethu Gonntshi, 33, who is unemployed and lives in a shanty with a friend. "Now, they will do what they like, and they will cripple us."

Gonntshi is like thousands of migrants who ended up in Alexandra. He was a farmer who left his wife and two young daughters in Eastern Cape two years ago to find steady work in Johannesburg. He says the only work he finds are temporary jobs unloading cargo from trucks, work that pays 75 rand - the equivalent of about $7.50 - a day. He was supposed to send money back home, but he says he barely has enough to feed himself.

"You can't feed a family on that," he says. "This is painful. South Africa is painful to live here."

But South Africa is a country of deep contrasts. In Sandton on Monday, Irene Dhlomo, 47, and friend Princess Thwala, 51, take photos on their iPads of the memorial to Mandela outside the Sandton city mall.

Dhlomo runs social economic development programs for a mining company that builds schools, roads and other infrastructure in the towns where the company does business. She has a three-bedroom luxury apartment in Sandton and two houses in her hometown of Kimberley in the Northern Cape.

In the days of apartheid, the government took her family's land and demolished their home. She lived with her nine brothers and sisters and her parents in a two-room house with no running water. They used buckets to go to the bathroom. Her saving grace, she says, was a scholarship that allowed her to get a degree in human resources.

"We were poor," she says. "There is a history of no education in my family, but education was the only liberator for me."

Thwala tells a similar story of poverty under apartheid. She says she went to Zimbabwe and later the USA on a scholarship to study engineering.

She says the country needs to provide basic infrastructure to many people, including better schools, health services, indoor plumbing and electricity, but she says the progress she and Dhlomo represent cannot be understated.

"My needs are not the same as a person in Alex, and I feel for them because during the days of apartheid, I lived in a similar area," she says. "But you have to look at the totality. And there's been a huge improvement."

They say young people who did not experience the oppression and brutality of life under apartheid have a harder time understanding how much better their lives are.

Michael Niosikili, 26, says he appreciates Mandela's message of self-reliance and hard work, but he looks around at his life in Alex, where he lives with his brothers and aunt and works a part-time job in a nearby store and sees how bad things are. It is midday, and he's hanging out in front of a grocery store across from Mandela's old house. He says he wants to go to college, but his family does not have enough money to send him.

"The living conditions are so bad - health, water, pollution, illegal connections for electricity that are dangerous. Here you see so much violence," he says. "People live their lives. You get used to so much. But it's like you are living in a cage."

He sees the opulence in Sandton, the construction of buildings, the wide, well-maintained streets and wonders, "How can you build such things and people here are still living in these conditions?

"Alex is in the middle of the good life," he says. "We are surrounded by food, but we can't eat."